Remarks on q-Monotone Functions and the Bernstein polynomials

Ulrich Abel*, Dany Leviatan, Ioan Raşa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function f∈ C[0 , 1] , which is twice differentiable in [0, 1], imply that the function is q-monotone. This provides a partial answer to an open problem of the authors in a recent paper.

Original languageEnglish
Article number41
JournalResults in Mathematics
Issue number2
StatePublished - Apr 2023


  • Polynomial inequalities
  • functional inequalities
  • q-monotonicity


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